Notably, the increment in electronic relaxation rate, \(\Lambda \) , is observed at a temperature different from the superconducting transition temperature, defined as the onset temperature of time-reversal symmetry breaking, \(T_{\text{onset}}\)  = 2.2 K. With increasing temperature, a small dip-like feature in the \(\Lambda \)  is followed by the constant value above the transition temperature. The similar dip-like feature in relaxation channel with two temperatures, \(T_{\text{onset}}\)  and \(T_c\) , are also observed in the other TRSB skutterudites superconductors such as PrPt\(_4\) Ge\(_{12}\)  [1]}, Pr\(_{1-x}\) Ce\(_{x}\) Pt\(_4\) Ge\(_{12}\)  [2]}, Pr\(_{1-x}\) La\(_{x}\) Pt\(_4\) Ge\(_{12}\)  [3]} and recently in La\(_7\) Ni\(_3\)  [4]}. However, the exact reason behind the dip feature is not known and is believed to be associated with the multi-component nature of the superconducting order parameter. For our case of quasi-skutterudite Lu\(_3\) Os\(_4\) Ge\(_{13}\) , this is discussed later.
